One zombie-related comic book series that is going on right now in DC Comics is called "The Blackest Night." Basically, black rings are flying throughout the universe, attaching themselves to corpses, and reanimating them. The reanimated corpses are called Black Lanterns (this story is related to Green Lantern).

Each Black Lantern has all of the knowledge, abilities, and superpowers of that deceased person. The ones who are being reanimated are the ones closest the heroes and they are targeting those heroes. Rather than brains, the Black Lanterns are seeking out and feeding on those with strong emotions. They are also targeting those heroes who have come back from the dead (like Superman, The Flash [Barry Allen], Superboy [Conner Kent], and Kid Flash [Bart Allen]).